Question

mass of the earth is 6 into 10 to the power 24 kg and that of the moon is 7.4 into 10 to the power 22 kg in the distance between the earth and the moon is 3. 84 into 10 to the power 5 km calculate the force exerted by the earth and the moon

Answer 1

Here is the answer---

Given Conditions ⇒

Mass of the Earth(m₁) = 6 × 10²⁴ kg.
Mass of the Moon(m₂) = 7.4 × 10²² kg.
Distance between the Earth and the Moon(d) = 3.84 × 10⁵ km.
 = 3.84 × 10⁸ m.
Gravitational Constant(G) = 6.7 × 10⁻¹¹ Nm²/kg².


Using the Newton's law of Gravitation,

 F = G × m₁×  m₂ × /d².

F is the Force of Gravitation between the Earth and the Moon.
Substituting the Given Values in the Formula,
∴ F = (6.7 × 10⁻¹¹ × 6 × 10²⁴ × 7.4 × 10²²) ÷ (3.84 × 10⁸)²
⇒ F = (6.7 × 6 × 7.4 × 10¹⁹) ÷ (14.7456)
⇒ F = 20.1741 × 10¹⁹ N.
⇒ F ≈ 20.2 × 10¹⁹ N.


Thus, the Gravitational Force of Attraction between the Earth and the Sun is 20.2 × 10¹⁹ N.

hope it helps u

Answer 2

Mass of the earth is 6 × 10²⁴ Kg and that of the moon is 7.4 × 10²² Kg and the distance between the earth and the moon is 3.84 × 10⁵ km.  

We have to find the force exerted by the earth and the moon.

According to Newton's Gravitational law,

" Gravitational force is the product of mass of bodies and inversely proportional to the square of distance between the bodies. "

i.e., F = (G × m₁ × m₂)/r²

here, m₁ = 6 × 10²⁴ Kg , m₂ = 7.4 × 10²² Kg and r = 3.84 × 10⁵ km = 3.84 × 10⁸ m

⇒ F = (6.67 × 10⁻¹¹ × 6 × 10²⁴ × 7.4 × 10²²)/(3.84 × 10⁸)²

= 2.0083 × 10²⁰ N ≈ 2 × 10²⁰ N

Therefore the force exerted by the earth and the moon is 2 × 10²⁰